Beta adjustment for leveraged index products

ABSTRACT

A technique to provide a return from an aggregate of an investment in a cash equivalent account and a leveraged index product account over a time period that is substantially equivalent to a multiple of the return of a theoretical position in an underlying index for the period of time is provided by calculating in a computer system a benchmark exposure of the theoretical position in the underlying index corresponding to the index used in the leveraged index fund; and based on the benchmark exposure, determining whether to initiate a transaction to re-allocate funds from the leveraged index product to a cash equivalent account or from the cash equivalent account to the leveraged index product according to the determined daily benchmark exposure.

BACKGROUND

This invention relates to leveraged index products and, in particular,leveraged mutual funds and leveraged exchange traded funds (ETF's).

Traditional index funds allow an investor to invest in a singleinstrument that generally replicates the performance of a benchmarkindex. Leveraged index products, on the other hand, seek to return amultiple of the return of an underlying benchmark over a period of timethat generally coincides with the frequency of the product'sdetermination of its net asset value.

Generally, leveraged index funds seek to return a multiple of the dailyreturn of an underlying index because these funds are required tocalculate a daily net asset value. Each calculation of net asset valueyields a new level of net assets and, therefore, a new base upon whichthe multiple of the return is based.

The extent to which a leveraged index product provides a multiple of thereturn of the benchmark index is generally referred to as the “Beta” ofthe product. For example, the Direxion S&P 500° Bull 2.5× Fund aims toprovide a return that is 2.5 times (e.g., 250%) the daily return of theS&P 500 Index and thus is a Fund with a beta of 2.5.

Leveraged index products attempt to achieve the stated return byproviding exposure to the benchmark in an amount equal to the product ofthe beta of the fund and the fund's net assets each day. For instance,if an investor makes a $100,000 investment in the Direxion S&P SOO® Bull2.5×, at the net asset value on a given day, the investor will receivethe equivalent of $250,000 of exposure to the S&P 500 Index® for thefollowing day. If the value of the S&P 500 Index® rises by 1% the nextday, the 1% gain on the $250,000 of exposure would translate into a gainof 2.5% on the investor's $100,000 investment. Conversely, if the S&P500 Index® declines 1%, the 1% loss on the $250,000 of exposure wouldtranslate into a 2.5% loss on the investor's $100,000 investment.

SUMMARY

Leveraged index products seek to provide a return which is a multiple ofthe return of a target index for a stated, limited period of time.However, the return of a leveraged index product for a period longerthan the stated, limited period is not necessarily equivalent tomagnifying the return of the benchmark by the relevant multiple for theperiod of time. That is, compounding successive, magnified periodicreturns introduces a path dependency that impacts returns for periodslonger than the stated limited period of time.

According to an aspect of the present invention, a computer implementedmethod includes periodically calculating in a computer system, atheoretical position in an underlying index corresponding to an indexused. in a leveraged index product account and based on the theoreticalposition, determining the level of investment in a leveraged indexproduct account that is required to provide substantially the sameexposure to the underlying index as the exposure provided by thetheoretical position in the underlying index.

The following are embodiments within the scope of the invention.

The method includes determining whether to initiate a transaction tore-allocate funds from the leveraged index product account to a cashequivalent account or from the cash equivalent account to the leveragedindex product account according to the determined theoretical positionin the underlying index. The method includes executing the determinedtransaction to re-allocate funds between the leveraged index productaccount and the cash equivalent account according to the determinedtheoretical position in the underlying index. The method attempts toprovide a return from the aggregate investment in the cash equivalentand the leveraged index product account that is substantially equivalentto a multiple of the cumulative return of the theoretical index over theperiod of time.

Calculating the theoretical position includes calculating a TheoreticalBenchmark Exposure by selecting a model to provide the exposure of thetheoretical position in the underlying index corresponding to the indexused in the leveraged index fund.

Determining whether to initiate a transaction includes determining adesired investment in a leveraged index product based on the theoreticalposition in the underlying index, comparing the desired investment inthe leveraged index product to the current value of funds in theleveraged index product and, if the current value exceeds the desiredvalue by more than a specified tolerance, sending a message to recommenda transfer of funds from the leveraged index product account to the cashequivalent account.

Determining whether to initiate a transaction includes determining adesired investment in a leveraged index product based on the theoreticalposition in the underlying index, comparing the desired investment inthe leveraged index product to the current value of funds in theleveraged index product account and, if current value exceeds thedesired value by more than a specified tolerance, the difference is morethan expected, using an automated system to transfer funds from theleveraged index product account to the cash equivalent account.

Determining whether to initiate a transaction includes determining adesired investment in a leveraged index product based on the theoreticalposition in the underlying index, comparing the desired investment inthe leveraged index product to the current value of funds in theleveraged index product and, if the desired value exceeds the currentvalue by more than a specified tolerance, sending a message to recommenda transfer of funds from the cash equivalent account to the leveragedindex product account.

Determining whether to initiate a transaction includes determining adesired investment in a leveraged index product based on the theoreticalposition in the underlying index, comparing the desired investment tothe current value of the funds in the leveraged index product and, ifthe desired value exceeds the current value by more than a specifiedtolerance, using an automated system to transfer funds from the cashequivalent account to the leveraged index product account.

The cash equivalent account is held in a money market account that islinked to the leveraged index product. The theoretical position in theunderlying index is a Theoretical Benchmark Exposure (TBE), which at anytime is determined according to:

(TBE)=K*P*(1+X)*((K−1)*(P)*(r)*(ip)).

where “P” is an amount of allocated assets; “K” is an leverage multipleof P; where the value of K is less than a beta of the leveraged fund;“X” is the return of the underlying index; “r” is the broker call rateand “ip” is the investment period.

The method includes monitoring the cash equivalent account and theleveraged index product account for determining whether to initiate atransaction. Periodic calculations occur on days when the leveragedindex product trades products that are based on the underlying index.

According to an additional aspect of the present invention, a computerprogram product residing on a computer readable medium for rebalancingexposure to an underlying index in a leveraged index product comprisesinstructions for causing a computer to periodically calculate in acomputer system, a theoretical position in an underlying indexcorresponding to an index used in a leveraged fund; and based on thetheoretical position, determine the level of investment in a leveragedindex product account that is required to provide substantially the sameexposure to the underlying index as the exposure provided by thetheoretical position in the underlying index.

According to an aspect of the present invention, an apparatus includes aprocessor and memory for executing along with the processor a computerprogram product. The apparatus also includes a computer readable mediumstoring the computer program product. The computer program product forrebalancing exposure to an underlying index in a leveraged index productcomprises instructions for causing a computer to periodically calculatein the computing system, a theoretical position in an underlying indexcorresponding to an index used in a leveraged fund; and based on thetheoretical position, determine the level of investment in an leveragedindex product account that is required to provide substantially the sameexposure to the underlying index as the exposure provided by thetheoretical position in the underlying index.

According to an aspect of the present invention, a memory for storingdata for access by an application program for managing leveraged indexproducts, the application program being executed on a data processingsystem includes a data structure stored in said memory, the datastructure including information resident in a database used by saidapplication program and including, a field identifying the leveragedindex product, a field identifying a cash account, a field identifying aleveraged index product account associated with the cash account, and afield identifying exposure rebalancing options for the leveraged indexproduct account.

One or more aspects of the invention may include one or more of thefollowing advantages.

The invention provides a mechanism to offset or counterbalance the pathdependency in pricing of leveraged index products, including daily betaleveraged index products.

The invention can re-allocate funds among cash or cash equivalents, andan account that holds a leveraged index product to provide a return fromthe aggregate over a time period that is substantially equivalent to amultiple of the return of the index over the period of time.

In essence, this provides a mechanism that permits investors to seekleveraged index returns for periods longer than the period for which theproducts attempt to provide such returns.

Based on a determined desired investment in a leveraged index productmessages to recommend a transfer of funds can be sent to request thetransfers or an automated system can be used to transfer funds betweenthe leveraged index product account and the cash equivalent account.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features,objects, and advantages of the invention will be apparent from thedescription and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a computer system.

FIGS. 2-5 are flow charts depicting processes for re-allocating exposurein leveraged products.

FIG. 6 is a diagram depicting exemplary transaction flow.

FIG. 7 is a diagram depicting a file or data structure stored on acomputer readable medium.

FIGS. 8-9 are diagrams depicting user interfaces.

FIG. 10 is a block diagram.

DESCRIPTION

Referring to FIG. 1, a computer system 10 includes a processor 12, mainmemory 14, storage 16, various interfaces 18 as well as I/O devices suchas a display 22 and keyboard 24 (as well as a mouse, etc.). The computersystem 10 also includes a network interface 26 that can be any networkinterface, such as Ethernet, dial up, wireless etc. As shown, the memoryhas an operating system 20 and application software 40 that are executedby the processor to assist with re-allocation assets of leveraged indexproducts, such as leverage index funds to provide exposure adjustmentscorrection, as discussed below.

The application software 40 can be configured to monitor investments inleveraged index funds that provide daily beta exposure. For example, thesoftware can work with the DirexionFunds® S&P 500® Bull 2.5× Fund, whichaims to achieve a daily return that is 2.5 times (e.g., 250%) of thedaily return of the S&P 500 Index®, an equities benchmark.

Although a single computer system 10 configuration, that is, a personalcomputer is shown, other configurations can be used such asclient-server configurations. In that situation, typically many suchserver systems could be in communication with client systems and thesoftware application can have client and server components that executeon the respective systems. In either situation, the computer system 10receives messages and data from other systems in order to determineexposure adjustments.

In addition, the application software 40 can be executed on differentcomputers, controlled by or managed by different entities that areinvolved in any of the aspects of leveraged index products. For example,in some embodiments, investors can use a tool as will be discussed belowto execute the application software 40, whereas in other embodimentsthis tool can be used by broker dealers that have control over customeraccounts invested in the leveraged product. In still other embodiments,the issuer of the leverage index products can use the applicationsoftware 40 and either apply the results of the execution of theapplication software 40 to the funds in their entirety or to thoseaccounts that it has access to or to generate messages to investorsand/or broker dealers to recommend transactions that result fromexecution of the software application. In still other embodiments,spreadsheets are used to aid in determination of exposure rebalancingpositions.

Understanding the Implications of Daily Betas

In general, open-ended products that offer daily or otherwise frequentliquidity cannot seek leveraged index returns for periods longer thanthe period between successive net asset value calculations because eachcalculation necessarily yields a new level of net assets thatnecessitates revised, magnified exposure to the benchmark performance.Generally, this period between successive calculations is daily (tradingdays in the market that trades the benchmark). Other periods could beused.

Changing exposure to the benchmark essentially starts a new period. Bychanging exposure to the benchmark, these changes have a compoundingeffect on exposure to the benchmark. Compounding of exposure causesdaily beta products to exhibit changes in exposure that are pathdependent. That is, for the same set of price changes in the benchmark,the exposure changes can be very different over the set of pricechanges, depending on the sequence which the price changes occur. As aconsequence, seeking daily returns has implications that are notintuitive, as will become apparent from the discussion below.

Table I shows: (A) the performance of a hypothetical benchmark, whichcould be, for instance, the S&P 500 Index®, over a period of four days;(B) 250% of the cumulative performance of the index at each point duringthe four days; and (C) expected return of a daily beta index product,e.g., the DirexionFunds S&P 500® Bull 2.5× Fund that seeks 250% of thedaily return of the index, the changes in net assets on each of the daysbased on the daily beta model (D) and a cumulative beta model (E).

TABLE I 2.5 Daily Beta Model 2.5 Cumulative Beta Model BenchmarkBenchmark Benchmark Daily Daily Beta Cumulative Daily Return X Model NetBenchmark Return X Theoretical Benchmark Return Beta = 2.5 AssetsCumulative Beta = 2.5 Net Assets Period Value (A) (B) (E) Return (C) (D)Day 0 100 100.00 Day 1 105 5.00% 12.50% 100.00 5.00% 12.5% 112.50 Day 2110 4.76% 11.90% 112.50 10.00% 25.00% 125.00 Day 3 115 4.55% 11.36%140.20 15.00% 37.5% 137.50 Returns 40.2% 37.5%

Table I shows that by providing a succession of daily returns equal to250% of the daily return of the benchmark results in a total return of40.20% for the leveraged fund, which is higher than the return of 37.50%for a theoretical position that provides 250% of the return of thebenchmark for the same period based on a cumulative Beta model.

TABLE II 2.5 Daily Beta Model 2.5 Cumulative Beta Model Leveraged IndexTheoretical Benchmark Net Benchmark Net Benchmark Benchmark Daily AssetsExposure Assets Exposure Period Value Return (F) (H) (G) (I) 100 100.00$250.00 100.00 $250.00 Day 1 105 5.00% 112.50 $281.25 112.50 $262.50 Day2 110 4.76% 125.89 $314.73 125.00 $275.00 Day 3 115 4.55% 140.20 $350.50137.50 $287.50

As shown in Table II, both the Daily Beta Model and the Cumulative BetaModel provide 250% of the return of the benchmark and have an initial$100.00 in assets (F) and (G) and consequently $250 of Leveraged IndexBenchmark Exposure (H) and Theoretical Benchmark Exposure (I) prior toDay One. Thus, the benchmark's 5% Day One gain increases the net assetsfrom $100.00 to $112.50 for both the Daily Beta Model and the CumulativeBeta Model.

At that point, the Daily Beta Model exposes 250% of the new Net Assetsto benchmark performance on Day Two. The resulting Leveraged indexBenchmark Exposure is ($112.50*2.5) $281.25. In contrast, the CumulativeBeta Model exposes 250% of the original $100 in assets to the benchmarkperformance for Day 2 but exposes only 100% of the gain, i.e., the$12.50, to the benchmark performance. As a consequence, the TheoreticalBenchmark Exposure on Day 2 is ($100*2.5+12.50) $262.50.

When the benchmark gains on Day Two, the Daily Beta Model's gains againare greater than those of the Cumulative Beta Model because theLeveraged Index Benchmark Exposure was greater than the TheoreticalBenchmark Exposure. The same is true on Day Three. The Daily Beta Modelthus provides more gains than the Cumulative Model for the Three Dayperiod.

When a benchmark declines sharply over three days, as the example belowshows, the Daily Beta Model declines less than the Cumulative Beta Model(−34.57% vs. −37.50%).

TABLE III Benchmark Benchmark Benchmark Daily Benchmark cumulativeBenchmark Daily Return X Fund Net cumulative return X Period ValueReturn Beta = 2.5 Assets return Beta Net Assets Day 0 100 100.00 100.00Day 1 95 −5.00% −12.50% 78.5 −5.00% −12.5% 87.50 Day 2 90 −5.26% −13.50%75.99 −10.00% −25.00% 75.00 Day 3 85 −5.56% −13.89% 65.43 −15.00% −37.5%62.50 Returns −34.57% −37.50%

As shown in Table IV below, both models have $100.00 in assets and $250in benchmark exposure prior to Day One (Day 0). The benchmark's 5% DayOne loss decreases net assets from $100.00 to $87.50 in both cases. TheDaily Beta Model, however, reduces exposure to the benchmark movement onDay Two, resulting in $218.75 of benchmark exposure. The Cumulative BetaModel, on the other hand, does not reduce exposure beyond the lossesalready incurred, so the Cumulative Beta Model has $237.50 in benchmarkexposure on Day Two.

When the benchmark declines on Day Two, the Daily Beta Model's lossesagain are less severe than those of the Cumulative Beta Model. The sameis true on Day Three, which is why the Daily Beta Model has betterperformance than the Cumulative Beta. Model for the three-day period.

TABLE IV 2.5 Daily Beta Model 2.5 Cumulative Beta Model Leveraged IndexTheoretical Benchmark Net Benchmark Net Benchmark Benchmark Daily AssetsExposure Assets Exposure Period Value Return (F) (H) (G) (T) 100 100.00$250.00 100.00 $250.00 Day 1 95 −5.00% 78.5 $218.75 87.50 $237.50 Day 290 −5.26% 75.99 $189.97 75.00 $225.00 Day 3 85 −5.56% 65.43 $163.5862.50 $212.50

Thus, one could conclude that the Daily Beta Models are inherentlysuperior to Cumulative Models because in up markets the performance ofDaily Beta Models (e.g., gains) is higher and in down markets theperformance (e.g., losses) is not as poor as that of the Cumulative BetaModels.

However, this is not necessarily true, because, as will be discussedbelow, the returns for each model are path dependent, e.g., the set ofprice movements that the benchmark takes during a period will havedifferent consequences for each of the models.

Since the Daily Beta models increases exposure in response to gains anddecreases exposure in response to losses, it has some inherentadvantages in markets which are linear and directional, i.e., days whenthe benchmark increases in value are followed in succession and dayswhen the benchmark decreases in value are followed in succession.However, most markets are not linear and are directional only overrelatively short periods of time.

For example, consider a market which is up and down but ultimately flat,as illustrated in the example of Table V.

TABLE V Benchmark Benchmark Benchmark daily Benchmark cumulativeBenchmark daily return X Fund net cumulative return X Period valuereturn Beta = 2.5 assets return Beta Net Assets 100 100.00 100.00 Day 1105 5.00% 12.50% $112.50 5.00% 12.50% $112.50 Day 2 100 −4.76% −11.90%$99.11 0.00% 0.00% $100.00 Day 3 105 5.00% 12.50% $111.50 5.00% 12.50%$12.50 Day 4 100 −4.76% −11.90% 98.22 0.00% 0.00% $100 (K) $ (L)

In this example, the Daily Beta Model provides losses (K), whereas theCumulative Model and the underlying benchmark show no change (L) overthe four day period.

This scenario can be explained by reference to Table VI.

TABLE VI 2.5 Daily Beta Model 2.5 Cumulative Beta Model Leveraged IndexTheoretical Benchmark Net Benchmark Net Benchmark Benchmark Daily AssetsExposure Assets Exposure Period Value Return (F) (H) (G) (I) Day 0 100$100.00 $250.00 $100.00 $250.00 Day 1 105 5.00% $112.50 $281.25 $112.50$262.50 Day 2 100 −4.76% $99.11 $247.77 $100.00 $250.00 Day 3 105 5.00%$111.50 $278.74 $112.50 $262.50 Day 4 100 −4.76% $98.22 $245.56 $100.00$250.00

As, shown in Table VI, both models have $100.00 in assets (M) and (N)and $250 in benchmark exposure (O) and (P) prior to Day One (Day 0), andwhen the underlying benchmark's gains 5%, the gain increases the netassets of both models from $100.00 to $112.50. However, the LeveragedIndex Benchmark Exposure on Day 2 is 250% of $112.50, or $281.25 whilethe Theoretical Benchmark Exposure is only $262.50. When the benchmarkdeclines on Day Two, the Daily Beta Model's losses are greater thanthose of the Cumulative Beta Model. In response to the decline in netassets caused by Day Two's losses, the Daily Beta Model reduces the netbenchmark exposure at day Three, a day when the market gains.

Responding to the increase in net assets due to gains on Day Three, theDaily Beta Model increases exposure, only to lose when the benchmarkdeclines on Day Four. Thus, on Day 4 with the benchmark back at theinitial value of 100 based on the decline of −4.76% on Day Four, theDaily Beta Model only has $98.22 of net assets, for exposure of only$245.56, whereas the Cumulative Model has assets of $100.00 for exposureof $250.00.

Application software 40 assists with exposure modification byrecommending re-allocation of assets between an investor's leveragedproduct account and cash or cash equivalent account. The applicationsoftware 40 is executed as a computer implemented process.

Referring to FIG. 2, high level features of the application software 40are illustrated. These features include calculating 40 a in a computersystem, an initial theoretical exposure to an underlying index given aninitial level of assets and a degree of magnification of such assets tothe relevant index. The application software also includes calculating40 b in a computer system, an initial investment in a leveraged indexproduct selected to provide a level of exposure to the underlying indexin an amount that is equivalent to the theoretical exposure determinedat 40 a. The application software also includes calculating 40 c anyimpact of changes in the index value and financing implications, if any,to determine a current theoretical exposure and calculating 40 d in acomputer system. the exposure to the underlying index provided by thecurrent value of the investment in the leveraged index product. Theapplication software also includes comparing 40 e the theoreticalexposure to the exposure provided by the current investment in theleveraged index product and, if there is a material difference,recommending (or initiating) 40 f purchases into, or redemptions from,the leveraged index product to attempt to ensure that the exposure tothe underlying index provided by the investment in the leveraged indexproduct is at least roughly equivalent to the theoretical exposure.

The application software 40 is a tool that an investor or other entitycan use to reallocate funds to balance market exposure in a leveragedproduct, such as a leveraged benchmark mutual fund to provide returnsthat are consistent with the market exposure the investor would have hadthe investor invested in a cumulative beta product.

In other words, referring back to Table II above, the applicationsoftware 40 in combination with execution of recommended transactionsprovides the investor's investment in the Fund with a Leveraged indexBenchmark Exposure that is substantially equal to the TheoreticalBenchmark Exposure of Table II (or Table IV).

The application software 40 permits investors, broker/dealers, issuers,and so forth, to re-balance exposure in accounts holding leveraged fundsin a manner that generates returns over a period of time that areequivalent to a multiple (“K”) of the cumulative total return of aTheoretical benchmark for the relevant period. The parameter “K” is apositive number for products that provide so called “long exposure,”whereas the parameter “K” is a negative number for products that provide“short exposure.”

Essentially, the multiplier K can have a range of values between theBeta of the leveraged index product and 0. (If the leveraged indexedproducts are paired (e.g., a pair of funds such as a Bull fund and aBear fund on the same benchmark), the multiplier K can have a range ofvalues between the Beta of the long product (Bull Fund) and the Beta ofthe short product (Bear Fund).

If the leveraged product is a long product (and has a positive Beta),the value of K is less than the Beta, to permit an allocation to cash ora cash equivalent so that Beta-K=MM can occur. If the leveraged productis a short product (and has a negative Beta), the value of K is greaterthan the Beta, to permit an allocation to cash or a cash equivalent sothat K-Beta=MM can occur.

In general, the value of K is a percentage of Beta. For leveragedproducts that have relatively high Betas or are based on benchmarks withrelatively high volatility, the value of K will generally be lower thanfor those leveraged products with relatively lower Betas or which arebased on benchmarks with relatively lower volatility. Thus, a relativelylow volatility fund could have K=0.85 B, whereas a higher volatilityfund might have a K=0.75 B. In general, K can be about 0.5 B to 0.9 B,more likely around 0.8 B.

Referring now to FIG. 3, specifics of an embodiment of the applicationsoftware 40 are described. The application software 40 receives oraccesses 42 a value “P”, which is the amount that the user (e.g.,investor, broker/dealer, issuer, etc.) chooses to allocate to thestrategy. The application software 40 also receives or accesses 44 thevalue “K” which is the leverage multiple that the investor desires toapply to P so that the Theoretical Benchmark Exposure is equal to K*P,where the symbol “*” here will be understood to correspond to amultiplication operation.

The application software 40 determines 46 whether K>1 or K<−1. The valueof K-i corresponds to that portion of the Theoretical Market Exposurethat is provided using leverage, and therefore will incur borrowingcosts. If, 1>K>−1, there is no leverage required. The cost of leverageis a factor in determining the Theoretical Benchmark Exposure becausethe cost of leverage reduces the Theoretical Benchmark Exposure.

Thereafter, the application software also receives 48 the value “X”,which is the benchmark return for the relevant period, the value “F”,the investment in the relevant leveraged product and the value “B,”which is the Beta of the relevant leveraged product.

The application software 40 calculates 52 a daily benchmark exposure ofa theoretical position (e.g., “Theoretical Benchmark Exposure” asdiscussed below). The application software 40 determines 54 a desiredinvestment (T) on each day, by dividing the determined benchmarkexposure, e.g., Theoretical Benchmark Exposure (TBE) value by B, thebeta of the leveraged product.

(T)=TBE/B

The application software 40 also multiplies the current investment (CI)in the investor's leveraged index product account by the Beta B of theleveraged index product to determine 58 the Leveraged Index BenchmarkExposure (LIBE).

(LIEBE)=CI*B

The Leveraged Index Benchmark Exposure (LIBE) is subtracted 58 from theTheoretical Benchmark Exposure and the difference between LeveragedIndex Benchmark Exposure and the Theoretical Benchmark Exposure. Thisdifference (LIBE)−(TBE) is divided by the Beta B of the leveraged indexproduct to determine an amount I_(d) by which the investment in theinvestor's leveraged index product account differs from the Theoreticalvalue or:

I _(d)=(LIBE−TBE)/B

If the difference I_(d)is substantial, 60 the software sends messages torecommend transactions (or in the case of an automated system placestrade(s)) 62.

Generally, the difference I_(d) between the current investment in theinvestor's leveraged index product account and the Theoretical BenchmarkExposure is expressed as a percentage of the current investment in theinvestor's leveraged index product account. Thus the difference I_(d)%expressed as a percentage is:

I _(d)%=I _(d)/CI

If the absolute value of the difference Id/CI is more than a thresholdpercentage, Q, then the messages or transactions will occur. Anexemplary range for Q can be 0.5% to 3%. However other ranges can beused. For instance, if transaction costs are minimal, the range can besubstantially lower than 0.5%, whereas if transaction costs are more ofa concern, the range could be higher than 3%, e.g. up to 5% or more. Inaddition, in those embodiments in which transactions are recommended,rather than automatically executed, even if the deviation is beyond therange, the messages will still be sent.

Referring now to FIG. 4, details 60 on how the application software 40determines the types of transfers or messages needed to rebalance theleveraged fund exposure to the underlying index are shown. Theapplication software 40, accesses 72 the difference percentage I_(d)% asdetermined above.

Recall that I_(d)=(LIBE−TBE)/B, and I_(d)%=I_(d)/CI if the differencepercentage I_(d)% indicates that the investment in the leveraged indexproduct is greater than 100%+Q of the target investment in the leveragedindex product, meaning the investment in the leveraged index productfalls outside the range on the high end, the application software 40will suggest 76 a transfer of assets from the Investor's Leveraged indexproduct to cash or cash equivalent or automatically transfer the assetsaccording to the preferences of the investor.

On the other hand, if the difference percentage I_(d)% indicates thatthe investment in the leveraged index product is less than 100%−Q of thetarget investment in the leveraged index product, meaning the investmentin the leveraged index product falls outside the range on the low end,the application software 40 will suggest. 78 a transfer of assets fromthe Investor's cash or cash equivalent to the leveraged index product orautomatically transfer the assets according to the preferences of theinvestor. In other situations 79 there are no recommendations ortransfers needed.

Thus, the Theoretical Benchmark Exposure TBE is used to rebalanceexposure in a leverage product by allocation of a portion of the assetsin the leveraged product to a money market account or vice versa basedon movements in the underlying benchmark that the leveraged producttracks.

The application software 40 can automatically move funds into and out ofa position in order to mimic the baseline investment on a periodic basisor these changes can be performed manually by a user. Exposurecorrection is accomplished by using an estimated closing value of theindex to compute the cumulative return from the start of the investment.

Theoretical Benchmark Exposure

Referring now to FIG. 5, determination of the TBE (Theoretical BenchmarkExposure) is shown. initially, the investor, broker/dealer, issuer, etc.selects a model by which insufficient or excess exposure of theleveraged product to changes in the underlying benchmark will bedetermined. Such a model should provide a benchmark that takes intoconsideration various real-world investment options for the investor.

One such model is discussed below. Other models could be used. Thismodel is referred to herein as “Theoretical Benchmark Exposure” model,as discussed above. An assumption underlying the Theoretical BenchmarkExposure model is that an investor seeking and benchmark return caninvest in a traditional benchmark product and can theoretically leveragethat return by committing its own principal and borrowed principal,i.e., money. In this scenario, K>1, and the investment is divided intoprincipal (“P”) and an investment made on margin (borrowed money)(P*(K−1)). The portion of the investment made on margin will incurinterest expense.

The return that is generated by this investment in the benchmark usingprincipal and margin provides a baseline return. The beta adjustment ofthe leveraged benchmark product seeks returns that are equivalent tothose of this baseline return provided by the Theoretical BenchmarkExposure model by recommending transactions among the relevant leveragedfunds and cash accounts, e.g., interest bearing accounts such as moneymarket accounts.

The Theoretical Benchmark Exposure is initially K * P and the grossTheoretical Benchmark Exposure at any subsequent point in time is(K*P*(1+X)). The gross Theoretical Benchmark Exposure is reduced byborrowing costs associated with the leveraged portion of the TheoreticalBenchmark Exposure (the money borrowed to provide the leverage). TheTheoretical Benchmark Exposure is not the theoretical value of theinvestor's investment position at a given time, but rather theTheoretical Benchmark Exposure is the theoretical exposure to thebenchmark at a given time.

Therefore, the Theoretical Benchmark Exposure at any time is determinedby accessing 82 the values of K, F, X, P, r and ip, as discussed above,and from these values calculating 84 Theoretical Benchmark Exposure as:

TBE=(K*P(1+X)−((K−1)*(P)*(r)*(ip))

where “r” is the broker call rate and “ip” is the investment period, asdiscussed above.

Thus, if a leveraged index benchmark seeks a daily return which is themultiple of the return of a benchmark (e.g., the

“TME”) and the beta “B” of the leveraged benchmark is greater than thedesired return “K”, the initial desired market exposure (T) of aninvestment strategy K*P is

K*P/B

with P−P*K/B being allocated to an interest bearing MM Fund.

On the other hand, the total market value (TMV) of the Leveraged Fundbased on the beta adjustment strategy discussed above is the CurrentValue in the Investor's Leveraged Fund Account and investor's MoneyMarket Account or:

TMV=CV+Mkt

Money market interest is accounted and the money market balance iscomputed using an interest rate that is compounded daily.

The application software 40 computes the total exposure of thetheoretical position (P*k*x where k=the return multiplier and x iscumulative return).

As discussed above, the amount “P” is defined as the amount of assetsthat e.g., the investor chooses to allocate to the strategy and thevalue “K” is a multiple of P that the investor desires. Therefore, theTheoretical Market Exposure (TME) is equal to K*P.

The accounting for the cost of margin can be determined by using theBroker Call Rate for each date of the investment period and determiningan average daily rate for the investment period by adding the rates foreach day from the start date until the current date, and dividing thesum by the number of days, and dividing that sum by 250 (the typicalnumber of trading days in a year). This average daily rate will bemultiplied by (K−1) P to determine the implicit interest expense.

Beta Adjustment Tool

Referring now to FIG. 6, an investor 102 interacts with a broker/dealer104 to view and manage the investor's assets/shares in a user's account109 containing Investor's Leveraged Fund Account 108 and correspondingInvestor's Money Market Account 110.

Although a single user, e.g., investor account is shown, it is to beunderstood that this is merely a simplification for illustrationpurposes. Money in all user's accounts resides in a Leveraged Fund 120,an investment pool comprised of funds from a plurality of investoraccounts. Some of these accounts can have an Investor Leveraged FundAccount 108 and a corresponding Money Market Account 110, for investorsthat chose to use a re-allocation tool. Others of these accounts mayonly have the Investor Leveraged Fund Account 108 for those investorsthat do not want to participate in re-allocation.

This investment pool is invested on a daily basis in a leveraged manneraccording to various investment strategies adopted by the particularfund. Money that is in money market accounts (or cash, or cashequivalents) can be considered part of the Leveraged Fund 120, but isnot part of the investment pool that is exposed in the leveraged manner.

Additionally, the Investor Leveraged Fund Account 108 can be processedindividually, in that the Leveraged Fund 120 makes transactions only forthose investors that indicate that the transactions are desired.

The tool includes a registration process (not shown) to allow aninvestor to register with the system and a login to allow the investorto login and access positions in the user's account containing theuser's leveraged fund positions 109, e.g., the Investor's Leveraged FundAccount 108 and corresponding Investor's Money Market Account 110.

Through a user interface, (FIG. 8), the investor 102 sends messages tothe broker 104 to execute, e.g., “buy trades” to allocate more fundsinto the Investor's Leveraged Fund Account 108 from the correspondingInvestor's Money Market Account 110, by transferring funds from theInvestor's Money Market Account 110 to the leveraged fund 120, as shown.In that case, money is transferred from the Investor's Money MarketAccount 110 to the issuer to purchase more assets from the LeveragedFund 120, and messages are returned adding those funds to the Investor'sLeveraged Fund Account 108.

Conversely, the messages (not shown) can transfer funds out of theInvestor's Leveraged Fund Account 108 into the corresponding Investor'sMoney Market Account 110, in which case funds in the leveraged fund. 120are removed. from the Fund 120 and transferred to the correspondingInvestor's Money Market Account 110 and removed from the investor'sLeveraged Fund Account 108. In one embodiment, the investor receivesmessages from the broker 104 that suggests which types of transfers tomake, if any, depending on market conditions.

Referring now to FIG. 7, a data structure and/or a file or object 120can be used to maintain user account information. In addition toconventional information that can be maintained for the user, e.g.,investor information, 122 a, identification of the particular leveragedfund, 122 b, identification of the underlying benchmark, 122 c, the datastructure 120 can include fields for exposure rebalancing options 122 dfor the account, and a linkage 122 e to the underlying money marketaccount (or equivalent) if the data structure 120 has enabled exposurerebalancing.

Referring to FIG. 8, a user interface 140 for the beta adjustment toolincludes a field 142 to allow an investor through a broker dealer, fundissuer, etc., to choose a benchmark, a field 144 to choose returnmultiple, a field 146 to specify an initial investment amount, and afield 148 to allow the user to re-balance exposure. This interface canbe part of a tool. that allows a user to initiate a new investment.

Other interfaces can be provided to allow the investor to thereaftertrack orders to be placed for the fund.

In subsequent user interfaces, after the user accesses the account, thetool provides exposure correction information to obtain up-to-dateexposure correction trades to execute to accomplish the exposurecorrection strategy and to record exposure correction trades. The toolalso allows a user to liquidate the investment.

Initiation of New Investment

Upon selection of the “Initiate new position” option, the system willallow the user to select a benchmark, an outlook (e.g., bullish orbearish) and enter the desired return multiple (K) and initialinvestment (P). Money market interest and margin interest rate can alsobe specified or system estimated default values can be accepted. Thesystem will use the benchmark and outlook to determine the leveragedfund to be purchased. This menu driven process permits a user to obtainthe correct leveraged fund from, e.g., a family of such funds that havedifferent characteristics, such as outlook, benchmark, and leverage.

The system allows the user to select the starting date, end date(default present), reallocation interval (daily, weekly, monthly, etc.)for an historical scenario. The same information is collected as in the“Initiate new position” feature (benchmark, outlook, K, P) above. Thesystem will process the scenario using the exposure correction discussedabove, generating a detailed view of the periodic investmentreallocation activities and the net results (benchmark move, netinvestment return, capital costs, etc).

Exposure Correction

Referring now to FIG. 9, an exposure correction user interface 140 isshown. This user interface 140 displays a listing 142 of all funds andexposure correction trades that need to be made. The exposure correctionuser interface 140 originates from a broker/dealer system 160 (FIG. 9)or the issuer's system 164 (FIG. 9). Such system (162, 164) generatesthe screens based on a feed of current day market movements.

In one embodiment, the system 160 or 164 does not auto-update the screenbecause if the user places trades well before closing, the exposurecorrection displayed when the user accepted the trade may be differentfrom exposure correction based on market closing values.

Referring now to FIG. 10, an exemplary arrangement is shown. In thisarrangement a broker dealer system 162 is in communication with anissuer's system 164 and a user's (e.g., investor's) system 166. Inresponse to the user clicking a “submit” for exposure correction orders146 (FIG. 9) of a given position, the broker/dealer 162 (or issuersystem 164) will record in dollars the amount of funds (leveraged fund108 and money market account 110) being purchased or sold in the user'saccount 109, as maintained on the broker/dealer's system 164.

Upon receipt of a net asset value message at the close of market, thesystem 164 will compute the new share balance in the leveraged fundaccount 108 for that investor. The system 164 will send messages to theinvestor's system 166, to display the investment allocation between theleveraged fund 108 and the money market 110 for that investor. Thebroker/dealer 164 (or issuer system 162) records the closing value ofthe benchmark to use as the base for computing cumulative returns.

There are recurring processes that occur in administration of useraccounts by broker dealers, and/or issuers. For instance, the dailyBroker call rate will be globally recorded for future Theoretical MarketExposure calculations. The index values are recorded daily to maintainthe ability to perform the transactions.

Integrated Beta Adjustment Trading

The beta adjustment tool can be integrated with a trading platform. Inone manner, the integration can be such that investors who are notinterested in the beta adjustment strategy are unaffected, whereas,investors seeking to initiate beta adjustments are able to use the sameconcepts and paradigms across traditional holdings and beta adjustmentmoldings.

Screens that display current holdings may show the beta adjustmentstrategy position as another fund distinct from any additional equitythat may be held in the same fund.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention. Forinstance, although the embodiments have been described with reference toequities and equity indexes, other leveraged products that are based onan index could use the tools described herein. For instance, theproducts could be bonds, commodities, real property and so forth.Accordingly, other embodiments are within the scope of the followingclaims.

1. A computer implemented method comprises: periodically calculating ina computer system, a theoretical position in an underlying indexcorresponding to an index used in a leveraged index product; and basedon the theoretical position, determining the level of investment in aleveraged index product account required to provide substantially thesame exposure to the underlying index as the exposure provided by thetheoretical position, with the exposure provided by the theoreticalposition being within a range of 0.5% to 5%; sending a messageindicating the level of investment to a user interface that isdisplayable on a user device, with the user interface having a field fora user to input a decision on the level of investment; and receiving aresponse from the user device indicated the user's decision.
 2. Themethod of claim 1, wherein the user interface is a graphical userinterface.
 3. The method of claim 1, further comprising: receiving fromthe user device a transaction message indicating a transaction toexecute; executing the transaction to re-allocate funds between theleveraged index product account and the cash equivalent account.
 4. Themethod of claim 1 wherein a return provided from the aggregate ofinvestment in the cash equivalent account and the leveraged indexproduct account over a time period is substantially equivalent to amultiple of the return of the theoretical position in the index over theperiod of time.
 5. The method of claim 1 wherein the user interfacecomprises: a field to allow an investor to choose a benchmark.
 6. Themethod of claim 2 wherein determining whether to initiate a transactionfurther comprises: determining a desired investment in a leveraged indexproduct based on the theoretical position in the underlying index;comparing the desired investment in the leveraged index product to thecurrent value of funds in the leveraged index product account to providea difference; and if the current value of funds in the leveraged indexproduct exceeds the desired value by more than a specified tolerance,sending the message to recommend a transfer of funds from the leveragedindex product account to the cash equivalent account.
 7. (canceled) 8.The method of claim 2 wherein determining whether to initiate atransaction further comprises: determining a desired investment in aleveraged index product based on the theoretical position in theunderlying index; comparing the desired investment in a leveraged indexproduct to the current value of funds in the leveraged index productaccount to provide a difference; and if the desired value of funds inthe leveraged index product exceeds the current value by more than aspecified tolerance, sending the message to recommend a transfer offunds from the cash equivalent account to the leveraged index productaccount.
 9. (canceled)
 10. (canceled)
 11. The method of claim 1 wherein,the theoretical position in the underlying index is a TheoreticalBenchmark Exposure (TBE), which at any time is determined according to:(TBE)=K*P*(1+X)*((K−1)*(P)*(r)*(ip)). where “P” is an amount ofallocated assets; “K” is an leverage multiple of P; where the value of Kis less than a beta of the leveraged fund; “X” is the return of theunderlying index; “r” is the broker call rate and “ip” is the investmentperiod.
 12. The method of claim 2 wherein the graphical user interfacefurther comprises: a field to choose return multiple, a field to specifyan initial investment amount, and a field to allow the user tore-balance exposure.
 13. (canceled)
 14. A computer program productresiding on a non-transitory computer readable medium for rebalancingexposure to an underlying index in a leveraged index product comprisesinstructions for causing a computer to: periodically calculate in acomputer system, a theoretical position in an underlying indexcorresponding to an index used in a leveraged fund; and based on thetheoretical position, determine the level of investment in a leveragedindex product account that is required to provide substantially the sameexposure to the underlying index as the exposure provided by thetheoretical position in the underlying index, with the exposure providedby the theoretical position being within a range of 0.5% to 5%; send amessage indicating the level of investment to a user interface that isdisplayable on a user device, with the user interface having a field fora user to input a decision on the level of investment and receive aresponse from the user device indicated the user's decision.
 15. Thecomputer program product of claim 14, further comprising instructionsto: generate the user interface that is a graphical user interface. 16.The computer program product of claim 14, further comprisinginstructions to: receive from the user device a transaction messageindicating a transaction to execute; execute the transaction tore-allocate funds between the leveraged index product account and cashequivalent account.
 17. (canceled)
 18. The computer program product ofclaim 14 wherein instructions to determine whether to initiate atransaction further comprise instructions to: determine a desiredinvestment in a leveraged index product based on the theoreticalposition in the underlying index; compare the desired investment in aleveraged index product to the current value of funds in the leveragedindex product account to provide a difference; and if the current valueof funds in the leveraged index product account exceeds the desiredinvestment by more than a specified tolerance, send the message torecommend a transfer of funds from the leveraged index product accountto the cash equivalent account.
 19. (canceled)
 20. The computer programproduct of claim 14 wherein instructions to determine whether toinitiate a transaction further comprise instructions to: determine adesired investment in a leveraged index product based on the theoreticalposition in the underlying index; compare the desired investment in aleveraged index product to the current value of the funds in theleveraged index product account to provide a difference; and if thedesired value of funds in the leveraged index product account exceedsthe current investment by more than a specified tolerance, send themessage to recommend a transfer of funds from the cash equivalentaccount to the leveraged index product account.
 21. The computer programproduct of claim 14 wherein the user interface further comprises a fieldto choose return multiple, a field to specify an initial investmentamount, and a field to allow the user to re-balance exposure. 22.(canceled)
 23. The computer program product of claim 14 wherein thetheoretical position in the underlying index is a Theoretical BenchmarkExposure (TBE) which is determined according to:(TBE)=K*P*(1+X)*((K−1)*(P)*(r)*(ip)). where “P” is an amount ofallocated assets; “K” is an leverage multiple of P; where the value of Kis less than a beta of the leveraged fund; “X” is the return of theunderlying index; “r” is the broker call rate and “ip” is the investmentperiod.
 24. A computing system comprises: a processor; and memory forexecuting along with the processor a computer program product; acomputer readable medium storing the computer program product, thecomputer program product for rebalancing exposure to an underlying indexin a leveraged exposure product comprises instructions for causing acomputer to: periodically calculate in the computing system, atheoretical position in an underlying index corresponding to an indexused in a leveraged index product; and based on the theoreticalposition, determine the level of investment in an leveraged indexproduct account that is required to provide substantially the sameexposure to the underlying index as the exposure provided by thetheoretical position in the underlying index, with the exposure providedby the theoretical position being within a range of 0.5% to 5%; send amessage indicating the level of investment to a user interface that isdisplayable on a user device, with the user interface having a field fora user to input a decision on the level of investment and receive aresponse from the user device indicated the user's decision.
 25. Thecomputing system of claim 24 wherein the user interface is a graphicaluser interface. 26-30. (canceled)
 31. The computing system of claim 24wherein the theoretical position in the underlying index is aTheoretical Benchmark Exposure (TBE) which is determined according to:(TBE)=K*P*(1+X)*((K−1)*(P)*(r)*(ip)) where “P” is an amount of allocatedassets; “K” is an leverage multiple of P; where the value of K is lessthan a beta of the leveraged fund; “X” is the return of the underlyingindex; “r” is the broker call rate and “ip” is the investment period.